Continuous higher order sliding mode control for a class of uncertain MIMO nonlinear systems: An ISS approach

In this article, we propose a new approach towards the design of higher order sliding mode (HOSM) control, for a class of multiple input multiple output (MIMO) uncertain nonlinear systems subject to matched and unmatched uncertainties. In the proposed method, nonlinear sliding surfaces incorporating the system initial conditions and exponential functions, which guarantee the existence of sliding mode from an initial state are utilized and appropriate control inputs are designed. The control inputs are designed to enforce second order sliding mode w.r.t the sliding variables via the use of multivariable super-twisting algorithm (STA) in finite time. The resulting sliding motion is in turn proved to be input-to-state-stable (ISS) with respect to the perturbations and unmatched uncertainties. The developed sliding mode control strategy is applied for the posture stabilization of a unicycle mobile robot. The proposed method is illustrated through simulations.